These taxes fund Medicare and Social Security which his administration and the GOP wants to cut back. Although reducing payroll taxes would be helpful to businesses, these programs may be necessary to help citizens infected or displaced by COVID-19. Medicare may need a buff to compensate for strain on the program if only for testing while those of retirement age (and more likely to be impacted by the virus) might opt to leave the workforce during this period and start drawing on their entitlements like Social Security. They have been paying into it their entire lives, they are entitled to now draw on those benefits.
Funny when you figure he's funding DOD spending to the tune of almost $1 trillion. Besides, the exalted Mitch McConnell has already nixed the idea of a payroll tax cut-funded stimulus.